Clearaudio Satisfy carbon tonearm front to back movement.

@mgolpoor, That is enough. You have to understand that this is a vibration measuring machine. It is designed to read the waveform in the groove that is in the thousandths of mm. Fiction in the groove wants to pull the tonearm forward but the friction varies with the intensity of modulation (called groove velocity). With this variation the arm can move back and forth causing all kinds of distortion. Some bearings can be tightened. Some can not. Vertical bearings are easy, the screws will be on the side at the fulcrum. You move the arm back and forth with you left hand and turn the screw clockwise until the arm just stops moving. The horizontal bearing is more difficult. It is usually not adjustable. 
Basically, if you can't fix it it s new tonearm time. The Clearaudio Magnify is a great arm and should fit right in.

Cleeds and I agree that unipivot arms are bad news. They are inherently unstable which is not good for any cartridge but particularly the less compliant cartridges we use today. Some cartridge manufacturers like Lyra specifically recommend against them. 

If it is similar to the current Satisfy Kardan then it should not be loose at all.
Even a proper uni pivot should not move in that direction unless you pick it up off the pivot. Easy movement in that direction is very bad and indicates a bad bearing which is never good. The best tonearms move in only two directions, up and down, and side to side. Nothing else.
I would get a new arm but that is up to you. My worry would be record wear from bad bearings. I am also not an expert in that arm.

@mgolpoor, How far is it moving in mm.